De Broglie Waves and Matter Wave Properties in Quantum Mechanics

What concept did Louis de Broglie extend to material particles in 1924?

The wave-particle dualism of light.

What does the de Broglie hypothesis state about moving particles?

Any moving particle is associated with a wave.

What are the waves associated with particles called?

De Broglie waves or matter waves.

How is the wavelength of matter waves related to the momentum of a particle?

The wavelength is inversely proportional to the magnitude of the momentum.

What is the de Broglie wavelength equation for a particle of mass m?

λ = h / p, where p is the momentum.

What is the relationship between wavelength and momentum for a photon?

λ = h / p, where p is the momentum of the photon.

What is the significance of the relation E = hv?

It connects the energy of a photon to its frequency.

What happens to the wavelength of matter waves as the mass of the particle decreases?

The wavelength increases, meaning lighter particles have longer wavelengths.

What type of waves are associated with particles, according to de Broglie?

Probability waves, not real three-dimensional waves like sound waves.

What is the kinetic energy expression for a charged particle accelerated by a potential difference V?

K.E. = eV.

What is the de Broglie wavelength for an electron accelerated by a potential difference V?

λ = h / √(2meV).

How is the de Broglie wavelength expressed in terms of kinetic energy K.E.?

λ = h / √(2mK.E.).

What is the kinetic energy of particles in thermal equilibrium at temperature T?

K.E. = (3/2)kT.

What is the relationship between the kinetic energy and de Broglie wavelength for particles in thermal equilibrium?

λ = h / √(3mK.E.).

What does the de Broglie hypothesis imply about the behavior of electrons?

Electrons can exhibit wave-like behavior under certain conditions.

What is the implication of the de Broglie wavelength for micro-particles?

The wave behavior is more pronounced for smaller, lighter particles.

What does the de Broglie hypothesis suggest about the dual nature of particles?

It suggests that particles have both wave and particle properties.